Global Existence of Solutions to the Timoshenko-Fourier System in Critical Besov Spaces

In this work, we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds, which admits a non-symmetric dissipation. Furthermore, the dissipative mechanism of regularity-loss type will occur in the case of non-equal wave speeds. We establish the global-in-time existence of solutions to the Timoshenko-Fourier system in critical Besov spaces with the regularity s= 3 2 .